JavaScript Program to print Fibonacci Series

The Fibonacci sequence is the integer sequence where the first two terms are 0 and 1. After that, the next term is defined as the sum of the previous two terms.

The recurrence relation defines the sequence Fn of Fibonacci numbers:

Fn = Fn-1 + Fn-2 with seed values F0 = 0 and F1 = 1

Examples:

Input : 5 
Output : 8
The first few Fibonacci Number are 0, 1, 1, 2, 3, 5, 8.....
Please note that 0th Fibonacci number is consider as 0. 
Therefore the 5th one is 8.

Input :8
Output :34

There are three methods to print the Fibonacci series, which are described below:

Approach 1: Using For loop

The for loop approach calculates the Fibonacci series by iteratively summing the previous two numbers, starting from 0 and 1. This method efficiently generates each Fibonacci number up to the desired term.

Example: In this example the function computes the nth Fibonacci number by iterating, updating two variables to store the last two numbers, and returning the nth number.

function fibonacci(num) {
    let num1 = 0;
    let num2 = 1;
    let sum;
    if (num === 1) {
        return num1;
    } else if (num === 2) {
        return num2;
    } else {
        for (let i = 3; i <= num; i++) {
            sum = num1 + num2;
            num1 = num2;
            num2 = sum;
        }
        return num2;
    }
}

console.log("Fibonacci(5): " + fibonacci(5));
console.log("Fibonacci(8): " + fibonacci(8));

Fibonacci(5): 3
Fibonacci(8): 13

Approach 2: Using While loop

The while loop approach generates the Fibonacci series by repeatedly summing the previous two numbers, starting from 0 and 1, until the desired term is reached, offering a straightforward and efficient iterative solution.

Example: In this example the function calculates the nth Fibonacci number using a while loop. It initializes the first two Fibonacci numbers and iterates to find the nth number, returning it.

function fibonacci(num) {
    if (num == 1)
        return 0;
    if (num == 2)
        return 1;
    let num1 = 0;
    let num2 = 1;
    let sum;
    let i = 2;
    while (i < num) {
        sum = num1 + num2;
        num1 = num2;
        num2 = sum;
        i += 1;
    }
    return num2;
}

console.log("Fibonacci(5): " + fibonacci(15));
console.log("Fibonacci(8): " + fibonacci(18));

Fibonacci(5): 377
Fibonacci(8): 1597

Approach 3: Using Recursion Method

The recursion approach generates the Fibonacci series by recursively summing the previous two terms, starting from the base cases 0 and 1. This method is simple but can be inefficient for large sequences without optimization.

Example: In this example the function uses recursion to calculate the nth Fibonacci number by summing the results of fibonacci(num - 1) and fibonacci(num - 2), with base cases for 1 and 2.

function fibonacci(num) {
    if (num == 1)
        return 0;
    if (num == 2)
        return 1;
    return fibonacci(num - 1) + fibonacci(num - 2);
}
console.log("Fibonacci(5): " + fibonacci(5));
console.log("Fibonacci(8): " + fibonacci(8));

Fibonacci(5): 3
Fibonacci(8): 13

Approach 4: Using Generator Function

Using a generator function, Fibonacci numbers are yielded incrementally. It maintains two variables representing the current and previous Fibonacci numbers. With each iteration, the next Fibonacci number is calculated and yielded, allowing for efficient memory usage and on-demand generation of the series.

Example: In this example the fibonacciGenerator function yields Fibonacci numbers using a generator. The fibonacci function iterates through the generator to get the nth Fibonacci number, returning the final result.

function* fibonacciGenerator(num) {
    let num1 = 0;
    let num2 = 1;
    yield num1;
    yield num2;
    for (let i = 3; i <= num; i++) {
        let sum = num1 + num2;
        num1 = num2;
        num2 = sum;
        yield num2;
    }
}

function fibonacci(num) {
    let result;
    const iterator = fibonacciGenerator(num);
    for (let i = 0; i < num; i++) {
        result = iterator.next().value;
    }
    return result;
}

console.log("Fibonacci(5): " + fibonacci(5));
console.log("Fibonacci(8): " + fibonacci(8));

Fibonacci(5): 3
Fibonacci(8): 13